Jkedrzej Garnek

activity

20192026

collaborators

8 papers

math.AG2026

The crystalline cohomology of covers with a cyclic $p$ -Sylow subgroup

Jędrzej Garnek

Let $X$ be a smooth projective curve over a field $k$ with an action of a finite group $G$ . A well-known result of Chevalley and Weil describes the $k [G]$ -module structure of cohom…

math.AG2025

The de Rham cohomology of covers with cyclic $p$ -Sylow subgroup

Jędrzej Garnek, Aristides Kontogeorgis

Let $X$ be a smooth projective curve over a field $k$ with an action of a finite group $G$ . A well-known result of Chevalley and Weil describes the $k [G]$ -module structure of cohom…

math.AG2024

Indecomposable direct summands of cohomologies of curves

Jędrzej Garnek

Groups with a non-cyclic Sylow $p$ -subgroup have too many representations over a field of characteristic~ $p$ to describe them fully. A~natural question arises, whether the world of…

math.AG2024

The "exponential" torsion of superelliptic Jacobians

Jędrzej Garnek

Let $J$ be the Jacobian of a superelliptic curve defined by the equation $y^{ℓ} = f (x)$ , where $f$ is a separable polynomial of degree non-divisible by $ℓ$ . In this article w…

math.AG2023

$p$ -group Galois covers of curves in characteristic $p$ II

Jędrzej Garnek

Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $G$ be a finite $p$ -group. The results of Harbater, Katz and Gabber associate a $G$ -cover of the projecti…

math.AG2022

$p$ -group Galois covers of curves in characteristic $p$

Jędrzej Garnek

We study cohomologies of a curve with an action of a finite $p$ -group over a field of characteristic $p$ . Assuming the existence of a certain 'magical element' in the function fiel…

math.NT2020

Number of points of certain Artin-Schreier curves

Jędrzej Garnek

We prove a conjecture of Johansen, Helleseth and Kholosha concerning equality of exponential sums related to the cross-correlation of $m$ -sequences. In the proof we show that certa…

math.AG2019

Equivariant splitting of the Hodge--de Rham exact sequence

Jędrzej Garnek

Let $X$ be an algebraic curve with an action of a finite group $G$ over a field $k$ . We show that if the Hodge-de Rham short exact sequence of $X$ splits $G$ -equivariantly then the…

The crystalline cohomology of covers with a cyclic p-Sylow subgroup

The de Rham cohomology of covers with cyclic p-Sylow subgroup

Indecomposable direct summands of cohomologies of curves

The "exponential" torsion of superelliptic Jacobians

p-group Galois covers of curves in characteristic p II

p-group Galois covers of curves in characteristic p

Number of points of certain Artin-Schreier curves

Equivariant splitting of the Hodge--de Rham exact sequence

The crystalline cohomology of covers with a cyclic $p$ -Sylow subgroup

The de Rham cohomology of covers with cyclic $p$ -Sylow subgroup

$p$ -group Galois covers of curves in characteristic $p$ II

$p$ -group Galois covers of curves in characteristic $p$